interesting prospects as an indirect method for estimating cloud amount in the polar regions, especially during the polar night. With the development of the International
Arctic Buoy Program, in particular, and the consequent availability of simultaneously measured surface-layer temperatures from various parts of the Arctic Basin, our method
could provide estimates of cloud amounts with coverage comparable to satellites.
4. Parameterizing the long-wave radiation balance in sea ice models
Long-wave radiation is one of the key processes determining the rate at which sea ice Ž
. forms in the polar regions in winter Maykut, 1986; Makshtas, 1991a . This fact has led
to numerous parameterizations for the long-wave radiation balance of snow-covered sea ice. These have, in turn, been used to study the climatic significance of processes
affecting ocean–atmosphere interaction in high latitudes, especially with coupled ocean–ice models in which the characteristics of the atmosphere are external parameters
Ž
. e.g., Hibler, 1979; Parkinson and Washington, 1979 .
Ž .
The long-wave radiation emitted by a surface F is described by the Stefan–Boltz-
up
mann law; F s ´s T
4
, 5
Ž .
up
where T is the surface temperature, ´ is the emittance of the surface, and s is the
Stefan–Boltzmann constant. Ž
. The incoming long-wave radiation from the atmosphere F
can be determined by
dn
Ž .
an appropriate radiative transfer model Kondratyev, 1969; Curry and Ebert, 1992 . Using such models, however, requires data on the distribution of air temperature and
Ž .
humidity up to heights of at least 30 km. Therefore, since the works of Brunt 1952 and
˚
Ž .
Angstrom Geiger, 1965; Matveev, 1969 , F has been parameterized from standard
¨
dn
meteorological observations using its empirical dependence on cloud amount and on the temperature and humidity of the atmospheric surface layer. In these parameterizations,
the incoming long-wave radiation is estimated from F s ´
n, T , e s T
4
, 6
Ž .
Ž .
dn
where ´ is the effective long-wave emittance of the atmosphere, a function of cloud
Ž . Ž .
amount and air temperature T and vapor pressure e at a height of 2 m. Many functional expressions for the effective emittance of the atmosphere have been
published. These are generally based on readily available observations and contain empirical coefficients obtained with a variety of temporal averaging methods. We
consider here the functions used most frequently.
4.1. Brunt’s method Ž
. Ž .
In the parameterization of Brunt 1952 e.g., Matveev, 1969 , ´
for a clear sky depends only on the water vapor content of the atmosphere and is described by
´ s a q b e
1r2
, 7
Ž .
B B
where e is the vapor pressure in millibars, and a and b
are empirical coefficients.
B B
On the basis of observations in middle latitudes, Brunt found a s 0.526 and
B
Ž .
b s 0.065. These coefficients, however, are not universal; Kondratyev 1969 shows
B
that their values change with the measurement site. Below we will show Marshunova’s Ž
. 1961 confirmation of this site dependence.
Ž .
Brunt deduced the long-wave radiation balance B s F y F
by introducing a
up dn
cloud multiplier. That is, the long-wave radiation balance in the presence of clouds is B s B 1 y c n ,
8
Ž .
Ž .
B
where n is fractional total cloud amount, B is the long-wave radiation balance for a clear sky, and c
is the average weighting coefficient for all types of clouds. For
B
Ž .
latitudes above 608N, c s 0.81 Berliand, 1956 .
B
4.2. MarshunoÕa’s method Ž
. The parameterization of Marshunova 1961 essentially applies Brunt’s methods to
meteorological conditions in the Arctic. The coefficients a and b
are different,
M M
however, and accounting for the influence of clouds occurs directly in the formula for F :
dn
´ s a q b e
1r2
1 q c n , 9
Ž .
Ž .
Ž .
M M
M
where n is again the fractional total cloud amount. Tables 6 and 7 list the a , b , and
M M
c coefficients that Marshunova obtained from monthly averaged values of B and n
M
observed at several polar stations and on drifting stations NP-3 and NP-4 in 1954–1957. Ž .
We see from Tables 6 and 7 that the empirical coefficients in Eq. 9 have clear Ž
spatial and temporal variability and are, thus, not universal. The variations in c Table
M
. 7 are especially pronounced. The variability in a , b , and c
is likely connected
M M
M
with the types of air masses and clouds prevalent in a region, a variability we earlier documented in Table 1.
4.3. Maykut and Church’s method On analyzing 3000 hourly observations of air temperature, humidity, incoming
long-wave radiation, and cloud amount collected during a year at Barrow, AK, Maykut
Table 6 Ž .
Ž .
The coefficients a and b
for use in Eq. 9 , derived by Marshunova 1961 from observations at various
M M
Arctic stations a
b
M M
Tikhaya Bay 0.61
0.073 Cape Zhelaniya
0.61 0.073
Chetyrekhstolbovoy Island 0.69
0.047 Cape Schmidt
0.69 0.047
NP-3, NP-4, 1954–1957 0.67
0.050
Table 7 Ž .
Ž .
Monthly averages of the coefficient c for use in Eq. 9 , derived by Marshunova 1961 from observations at
M
various Arctic stations J
F M
A M
J J
A S
O N
D Tikhaya Bay
0.27 0.29
0.29 0.24
0.24 0.22
0.19 0.19
0.21 0.25
0.26 0.28
Cape Zhelaniya 0.29
0.29 0.29
0.24 0.24
0.22 0.19
0.18 0.21
0.22 0.26
0.28 Chetyrekhstolbovoy Island
0.27 0.27
0.25 0.24
0.22 0.19
0.16 0.19
0.22 0.25
0.25 0.27
Cape Schmidt 0.25
0.25 0.20
0.25 0.24
0.18 0.16
0.19 0.22
0.25 0.27
0.26 NP-3, NP-4, 1954–1957
0.30 0.30
0.30 0.28
0.27 0.24
0.22 0.23
0.27 0.29
0.30 0.30
Ž .
and Church 1973 developed the following expression for the effective emittance of the polar atmosphere:
´ s 0.7855 1 q 0.2232 n
2 .75
, 10
Ž .
Ž .
where, as above, n is the fractional total cloud amount. The difference between this and previous parameterizations is that here the influence of water vapor on incoming
long-wave radiation is taken into account indirectly in the empirical coefficients.
4.4. Satterlund’s method Ž
. For parameterizing the effective emittance, Satterlund 1979 offers a function of air
Ž .
temperature and vapor pressure that Brutsaert 1982
claims describes long-wave radiation well at low temperatures:
T r2016
´ s 1.08 1 y exp ye ,
11
Ž .
Ž .
where T is in kelvins and e is in millibars. As with Brunt’s method, Satterlund accounts Ž .
for cloud effects by using a multiplier in the long-wave radiation balance as in Eq. 8 . 4.5. Konig-Langlo and Augstein’s method
¨
Ž .
For effective emittance, Konig-Langlo and Augstein 1994; henceforth, KL A
¨
suggest ´ s a q b n
3
, 12
Ž .
K K
where n is again the fractional total cloud amount, and a and b
are empirical
K K
coefficients. As in Maykut and Church’s parameterization, these a and b
coefficients
K K
implicitly include humidity effects. KL A obtained a s 0.765 and b s 0.22 on the basis of visual observations of
K K
cloud amount and measurements of incoming long-wave radiation with an Eppley PIR
˚
X
Ž pyrgeometer at two polar stations
Ny-Alesund, 70856 N, 11856E; and Georg von
X X
. Neumayer, 70839 S, 8815 W . KL A’s ´
differs from Maykut and Church’s by its stronger dependence on cloud amount.
4.6. New test of the long-waÕe parameterizations The Russian NP drifting stations yielded many observations of the long-wave
Ž .
radiation balance. Marshunova and Mishin 1994 recently described the sensors used for these observations and their accuracy and tabulated monthly averaged data. For this
work, we created, from the original archived Russian data, a new data set consisting of 3-hourly radiation measurements made on NP-4 in 1956–1957. Together with the
surface-level air temperature data included on the National Snow and Ice Data Center Ž
. 1996 CD-ROM, this radiation data lets us test our cloud algorithm and the emittance
formulas described above for the central Arctic. We also obtained new data for additional tests during the drift of the Russian–
Ž American ISW in the western Weddell Sea from February to June 1992 Andreas et al.,
. 1992; Claffey et al., 1995 . During this period, in the center of a drifting 1-km-wide ice
floe, we made continuous, hourly averaged measurements of the components of the long-wave radiation budget and the usual meteorological variables with both Russian
and American sensors. The radiation measurements, in particular, showed good agree-
Ž .
ment among the various instruments Claffey et al., 1995 . Ž .
Fig. 10 shows the effective atmospheric emittance, computed from Eq. 6 with T taken as the 5-m air temperature, for all of our ISW data. The curve is the KL A
Ž .
relation, Eq. 12 . Because of the negligible increase in emittance for cloud amounts between 0 and 5 and the steep increase for cloud amounts of 9 and 10 in Fig. 10, no
emittance model that is linear in cloud amount, such as Brunt’s, Marshunova’s, or Satterlund’s, can fit the ISW data as well as nonlinear relations like KL A’s and
Maykut and Church’s.
Ž . Fig. 10. The effective atmospheric emittance, computed from Eq. 6 , based on all the ISW data collected from
25 February through 29 May 1992. The error bars show one standard deviation. The line is Konig-Langlo and
¨
Ž .
Ž .
Augstein’s 1994 relation, Eq. 12 .
Table 8 lists some statistics of the measurements for all of the observations made in May 1992 on ISW and in November 1956 on NP-4. We focus on May at ISW because
we have data for the entire month and because the short-wave components — which might complicate our measuring and interpreting the long-wave radiation — were small.
November in the Arctic is similar to May in the Antarctic — late fall. Because cloud
Ž .
amounts at ISW and at NP-4 had a U-shaped distributions Figs. 3 and 4 , Table 8 treats Ž
. Ž
. Ž
. the radiation values for clear 0–2 , partly cloudy 3–7 , and overcast 8–10 skies
separately, regardless of other weather conditions. On studying Table 8, we see that the values of long-wave radiation balance at the two
stations are very similar in both the mean and the standard deviation. We thus infer that the long-wave radiation balance is influenced similarly by clouds in both regions and
has similar seasonal values, at least when short-wave radiation is weak or absent. These are important points in light of the dependence on region and season of some of the
simple parameterizations described above.
Table 9 shows the results of our tests of the five long-wave parameterizations described above against both the ISW and NP-4 data. Again, we tabulate bias, random,
and total errors, as in Table 5. We see in Table 9 that, of the five incoming long-wave parameterizations that we are considering, the one by Konig-Langlo and Augstein
¨
Ž .
1994 performs best. Comparing the entries in Tables 8 and 9, we see that, for it, the total error for the difference between the measured values and those calculated with Eqs.
Ž . Ž
. 6 and 12 does not exceed 5, even for cloud amounts of 3–7 tenths, where the
random error caused by inaccuracies in the measurements is largest. Five percent is approximately the experimental error in the ISW F
values.
dn
Ž .
The parameterization of Maykut and Church 1973 perform almost as well as KL A’s, but the other three parameterizations for F
are significantly worse. The
dn
Table 8 Ž
Observed values of the long-wave radiation balance B and the incoming long-wave radiation F both in
dn y2
. W m
. The observations are from ISW in May 1992 and NP-4 in November 1956. ‘‘No. Obs.’’ is the number of observations for the indicated cloud amount, ‘‘Mean’’ is the average value for that cloud amount,
and ‘‘Std’’ is the standard deviation Ž
. Cloud amount tenths
ISW NP-4
No. Obs. B
F No. Obs.
B
dn
0–2 110
22 Mean
43 154
35 Std
5 13
6 3–7
269 12
Mean 24
181 30
Std 8
22 12
8–10 363
82 Mean
y1 225
1 Std
7 19
10 0–10
742 116
Mean 15
198 11
Std 18
34 18
Table 9 Values of the bias, random, and total errors in the long-wave radiation balance B and in the incoming
Ž
y2
. long-wave radiation F
both in W m when the May 1992 data from ISW and the November 1956 data
dn
from NP-4 are compared with five different incoming long-wave parameterizations. ‘‘Bias’’ is defined as the observation minus the parameterization
Method Cloud amount
ISW NP-4
Ž .
tenths Bias
Random Total
Bias Random
Total Ž .
Brunt, Eq. 7 0–2
B y30
3.5 30.2
y46 8
46.7 F
30 2.5
30.1
dn
3–7 B
y27 2.9
27.2 y17
4 22.0
F 27
2.5 27.1
dn
8–10 B
y25 4.4
25.4 y18
10 20.6
F 25
3.7 25.3
dn
0–10 B
y26 4.1
26.3 y23
15 27.6
F 26
3.6 26.2
dn
Ž . Marshunova, Eq. 9
0–2 B
y16 3.0
16.3 y20
7 21.2
F 14
2.2 14.2
dn
3–7 B
y25 4.5
25.4 y3
13 13.3
F 22
4.1 22.4
dn
8–10 B
y37 6.0
37.5 y13
13 18.4
F 34
5.5 34.4
dn
0–10 B
y30 9.5
31.5 y13
13 18.4
F 27
8.9 28.4
dn
Ž .
Maykut and Church, Eq. 10 0–2
B 4
4.2 5.8
y3 7
7.6 F
y6 3.4
7.0
dn
3–7 B
y11 6.2
12.6 y3
12 12.4
F 8
5.7 9.8
dn
8–10 B
y18 4.6
18.6 y11
11 15.6
F 14
3.7 14.4
dn
0–10 B
y12 9.2
15.1 y8
11 13.6
F 9
8.4 12.3
dn
Ž .
Satterlund, Eq. 11 0–2
B y17
2.8 17.2
y32 8
33.0 F
18 2.4
18.2
dn
3–7 B
y17 2.6
17.2 y8
14 16.1
F 18
2.1 18.1
dn
8–10 B
y20 4.5
20.5 y14
10 17.2
F 20
3.8 20.4
dn
0–10 B
y18 3.9
18.4 y17
12.5 21.2
F 18
3.7 18.4
dn
Ž .
KLA, Eq. 12 0–2
B 4
4.2 5.8
y7 8
10.6 F
y6 3.5
6.9
dn
3–7 B
y10 5.6
11.5 y6
13 14.3
F 8
5.0 9.4
dn
8–10 B
y11 4.9
12.0 y5
11 12.1
F 7
4.6 8.4
dn
0–10 B
y8 7.3
10.8 y6
11 12.5
F 5
6.7 8.4
dn
nonlinear dependence on clouds in the KL A and Maykut and Church formulations amplifies errors in the observations and produces random errors for these parameteriza-
Fig. 11. Measured incoming long-wave radiation during May 1992 on ISW and predictions of it using the equations of Brunt, Marshunova, Maykut and Church, Satterlund, and Konig-Langlo and Augstein. The upper
¨
panel is a temporal sequence when the total cloud amount was 8–10 tenths. Satterlund’s scheme produces estimates between the Brunt and Maykut and Church estimates and is, thus, left out of this panel for clarity.
The lower panel is for observations when the total cloud amount was 0–2 tenths. Because Maykut and Church’s scheme produces estimates similar to KLA’s and because Satterlund’s scheme yields results similar
to Marshunova’s, we leave these two traces out of this panel for clarity.
tions in Table 9 that are generally larger than for the other three parameterizations. But these random errors are fairly independent of cloud amount and thus, seemingly, result
from experimental uncertainties rather than faults in the parameterizations. For the other three parameterizations, in contrast, the random errors vary with cloud amount and, thus,
reflect shortcomings in these parameterizations.
Fig. 11 shows the temporal variability of the incoming long-wave radiation for May observed on ISW and estimated with the five parameterizations under consideration.
Although the estimates may differ from the observed radiation for both the clear-sky and overcast-sky cases, each of the five parameterization schemes does predict temporal
behavior that coincides with that in the experimental data.
On comparing the errors tabulated in Table 9 with the mean values in Table 8, we see Ž
. that the total error in evaluating B for clear skies cloud amounts of 0–2 tenths with the
KL A parameterizations is above 10 for ISW and about 30 for NP-4. If we Ž
. consider all the observations during the month 0–10 tenths , the total error increases to
Ž over 70 for ISW and to over 100 for NP-4. Notice, too, that for overcast skies 8–10
. Ž
. tenths , when the absolute values of B are small Table 8 , even the sign of B is
uncertain. Remember, though, the long-wave radiation balance — whether calculated as the difference between the incoming and emitted long-wave components, as on ISW, or
as measured directly with a single sensor, as on NP-4 — represents a small difference between large values of F
and F . As a result, it has a large relative error;
dn up
parameterizing it is consequently difficult. Nevertheless, data from both ISW and NP-4 confirm that KL A’s is the best among five alternatives for parameterizing the
long-wave radiation balance over sea ice during the polar night for the periods studied.
5. Model sensitivity to the description of long-wave radiation
